Basic properties
Modulus: | \(4001\) | |
Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2000\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4001.w
\(\chi_{4001}(9,\cdot)\) \(\chi_{4001}(18,\cdot)\) \(\chi_{4001}(29,\cdot)\) \(\chi_{4001}(31,\cdot)\) \(\chi_{4001}(33,\cdot)\) \(\chi_{4001}(36,\cdot)\) \(\chi_{4001}(45,\cdot)\) \(\chi_{4001}(47,\cdot)\) \(\chi_{4001}(61,\cdot)\) \(\chi_{4001}(62,\cdot)\) \(\chi_{4001}(66,\cdot)\) \(\chi_{4001}(72,\cdot)\) \(\chi_{4001}(83,\cdot)\) \(\chi_{4001}(89,\cdot)\) \(\chi_{4001}(90,\cdot)\) \(\chi_{4001}(94,\cdot)\) \(\chi_{4001}(97,\cdot)\) \(\chi_{4001}(111,\cdot)\) \(\chi_{4001}(116,\cdot)\) \(\chi_{4001}(117,\cdot)\) \(\chi_{4001}(118,\cdot)\) \(\chi_{4001}(122,\cdot)\) \(\chi_{4001}(124,\cdot)\) \(\chi_{4001}(126,\cdot)\) \(\chi_{4001}(137,\cdot)\) \(\chi_{4001}(138,\cdot)\) \(\chi_{4001}(145,\cdot)\) \(\chi_{4001}(149,\cdot)\) \(\chi_{4001}(155,\cdot)\) \(\chi_{4001}(165,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2000})$ |
Fixed field: | Number field defined by a degree 2000 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{467}{2000}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4001 }(122, a) \) | \(1\) | \(1\) | \(e\left(\frac{241}{500}\right)\) | \(e\left(\frac{467}{2000}\right)\) | \(e\left(\frac{241}{250}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{1431}{2000}\right)\) | \(e\left(\frac{119}{500}\right)\) | \(e\left(\frac{223}{500}\right)\) | \(e\left(\frac{467}{1000}\right)\) | \(e\left(\frac{3}{250}\right)\) | \(e\left(\frac{59}{80}\right)\) |